The Utility Function, Indifference Curves, and Healthcare

By Brennan T. Beal

Impetus For The Post

When I first learned about utility functions and their associated indifference curves, I was shown an intimidating figure that looked a bit like the image below. If you were lucky, you were shown a computer generated image. The less fortunate had a professor furiously scribbling them onto a board.

https://opentextbc.ca/principlesofeconomics/back-matter/appendix-b-indifference-curves/

A few things were immediately of concern: why are there multiple indifference curves for one function if it only represents one consumer? Why are the curves moving? And… who is Natasha? So, while answering my own questions, I thought sharing the knowledge would be helpful. This post will hopefully provide a better description than maybe most of us have heard and by the end you will understand:

  1. What indifference curves are and what they represent
  2. How a budget constraint relates to these indifference curves and the overall utility function
  3. How to optimize utility within these constraints (if you’re brave)

For the scope of this post, I’ll assume you have some fundamental understanding of utility theory.

Click here to link to my original post to continue reading.

Economic Evaluation Methods Part I: Interpreting Cost-Effectiveness Acceptability Curves and Estimating Costs

By Erik Landaas, Elizabeth Brouwer, and Lotte Steuten

One of the main training activities at the CHOICE Institute at the University of Washington is to instruct graduate students how to perform economic evaluations of medical technologies. In this blog post series, we give a brief overview of two important economic evaluation concepts. Each one of the concepts are mutually exclusive and are meant to stand alone. The first of this two-part series describes how to interpret a cost-effectiveness acceptability curve (CEAC) and then delves into ways of costing a health intervention. The second part of the series will describe two additional concepts: how to develop and interpret cost-effectiveness frontiers and how multi-criteria decision analysis (MCDA) can be used in Health Technology Assessment (HTA).

 

Cost-Effectiveness Acceptability Curve (CEAC)

The CEAC is a way to graphically present decision uncertainty around the expected incremental cost-effectiveness of healthcare technologies. A CEAC is created using the results of a probabilistic analysis(PA).[1] PA involves simultaneously drawing a set of input parameter values by randomly sampling from each parameter distribution, and then storing the model results.  This is repeated many times (typically 1,000 to 10,000), resulting in a distribution of outputs that can be graphed on the cost-effectiveness plane. The CEAC reflects the proportion of results that are considered ‘favorable’ (i.e. cost effective) in relation to a given cost-effectiveness threshold.

The primary goal of a CEAC graph is to inform coverage decisions among payers that are considering a new technology, comparing one or more established technologies that may include the standard of care. The CEAC enables a payer to determine, over a range of willingness to pay (WTP) thresholds, the probability that a medical technology is considered cost-effective in comparison to its appropriate comparator (e.g. usual care), given the information available at the time of the analysis. A WTP threshold is generally expressed in terms of societal willingness to pay for an additional life year or quality-adjusted life year (QALY) gained. In the US, WTP thresholds typically range between $50,000 – $150,000 per QALY.

The X-axis of a CEAC represents the range of WTP thresholds. The Y-axis represents the probability of each comparator being cost-effective at a given WTP threshold, and ranges between 0% and 100%. Thus, it simply reflects the proportion of simulated ICERs from the PA that fall below the corresponding thresholds on the X-axis.

Figure 1. The Cost-Effectiveness Acceptability Curve

CEAC

Coyle, Doug, et al. “Cost-effectiveness of new oral anticoagulants compared with warfarin in preventing stroke and other cardiovascular events in patients with atrial fibrillation.” Value in health 16.4 (2013): 498-506.

Figure 1 shows CEACs for five different drugs, making it easy for the reader to see that at the lower end of the WTP threshold range (i.e. $0 – $20,000 per QALY), warfarin has the highest probability to be cost-effective (or in this case “optimal”). At WTP values >$20,000 per QALY, dabigatran has the highest probability to be cost-effective. All the other drugs have a lower probability of being cost-effective compared to warfarin and dabigatran at every WTP threshold. The cost-effectiveness acceptability frontier in Figure 1 follows along the top of all the curves and shows directly which of the five technologies has the highest probability of being cost-effective at various levels of the WTP thresholds.

To the extent that the unit price of the technology influences the decision uncertainty, a CEAC can offer insights to payers as well as manufacturers as they consider a value-based price. For example, a lower unit price for the drug may lower the ICER and, all else equal, this increases the probability that the new technology is considered cost-effective at a given WTP threshold. Note, that when new technologies are priced such that the ICER falls just below the WTP for a QALY, (e.g. an ICER of $99,999 when the WTP is $100,000) the decision uncertainty tends to be substantial, often around 50%. If decision uncertainty is perceived to be ‘unacceptably high’, it can be recommended to collect further information to reduce decision uncertainty. Depending on the drivers of decision uncertainty, for example in case of stochastic uncertainty in the efficacy parameters, performance-based risk agreements (PBRAs) or managed entry schemes may be appropriate tools to manage the risk.

Cost estimates

The numerator of most economic evaluations for health is the cost of a technology or intervention. There are several ways to arrive at that cost, and choice of method depends on the context of the intervention and the available data.

Two broadly categorized methods for costing are the bottom-up methodand the top-down method. These methods, described below, are not mutually exclusive and may complement each other, although they often do not produce the same results.

costs

Source of Table: Mogyorosy Z, Smith P. The main methodological issues in costing health care services: a literature review. 2005.

The bottom-up method is also known as the ingredients approach or micro-costing. In this method, the analyst identifies all the items necessary to complete an intervention, such as medical supplies and clinician time, and adds them up to estimate the total cost. The main categories to consider when calculating costs via the bottom-up method are medical costs and non-medical costs. Medical costs can be direct, such as the supplies used to perform a surgery, or indirect, such as the food and bed used for inpatient care. Non-medical costs often include costs to the patient, such as transportation to the clinic or caregiver costs. The categories used when estimating the total cost of an intervention will depend on the perspective the analyst takes (perspectives include patient, health system, or societal).

The bottom-up approach can be completed prospectively or retrospectively, and can be helpful for planning and budgeting. Because the method identifies and values each input, it allows for a clear breakdown as to where dollars are being spent. To be accurate, however, one must be able to identify all the necessary inputs for an intervention and know how to value capital inputs like MRI machines or hospital buildings. The calculations may also become unwieldy on a very large scale. The bottom-up approach is often used in global health research, where medical programs or governmental agencies supply specific items to implement an intervention, or in simple interventions where there are only a few necessary ingredients.

The top-down estimation approach takes the total cost of a project and divides it by the number of service units generated. In some cases, this is completed simply looking at the budget for a program or an intervention and then dividing that total by the number of patients. The top-down approach is useful because it is a simple, intuitive measurement that captures the actual amount of money spent on a project and the number of units produced, particularly for large projects or organizations. Compared to the bottom-up approach, the top-down approach can be much faster and cheaper. The top-down approach can only be used retrospectively, however, and may not allow for the breakdown of how the money was spent or be able to identify variations between patients.

While the final choice will depend on several factors, it makes sense to try and think through (or model) which of the cost inputs are likely to be most impactful on the model results. For example, the costs of lab tests may most accurately be estimated by a bottom-up costing approach. However, if these lab costs are likely to be a fraction of the cost of treatment, say a million dollar cure for cancer, then going through the motions of a bottom-up approach may not be the most efficient way to get your PhD-project done in time. In other cases, however, a bottom-up approach may provide crucial insights that move the needle on the estimated cost-effectiveness of medical technologies, particularly in settings where a lack of existing datasets is limiting the potential of cost-effectiveness studies to inform decisions on the allocation of scarce healthcare resources.

[1]Fenwick, Elisabeth, Bernie J. O’Brien, and Andrew Briggs. “Cost‐effectiveness acceptability curves–facts, fallacies and frequently asked questions.” Health economics 13.5 (2004): 405-415.

Commonly Misunderstood Concepts in Pharmacoepidemiology

By Erik J. Landaas, MPH, PhD Student and Naomi Schwartz, MPH, PhD Student

 

Epidemiologic methods are central to the academic and research endeavors at the CHOICE institute. The field of epidemiology fosters the critical thinking required for high quality medical research. Pharmacoepidemiology is a sub-field of epidemiology and has been around since the 1970’s. One of the driving forces behind the establishment of pharmacoepidemiology was the Thalidomide disaster. In response to this tragedy, laws were enacted that gave the FDA authority to evaluate the efficacy of drugs. In addition, drug manufacturers were required to conduct clinical trials to provide evidence of a drug’s efficacy. This spawned a new and important body of work surrounding drug safety, efficacy, and post-marketing surveillance.[i]

In this article, we break down three of the more complex and often misunderstood concepts in pharmacoepidemiology: immortal time bias, protopathic bias, and drug exposure definition and measurement.

 

Immortal Time Bias

In pharmacoepidemiology studies, immortal time bias typically arises when the determination of an individual’s treatment status involves a delay or waiting period during which follow-up time is accrued. Immortal time bias is a period of follow-up during which, by design, the outcome of interest cannot occur. For example, the finding that Oscar winners live longer than non-winnersis a result of immortal time bias. In order for an individual to win an Oscar, he/she must live long enough to receive the award.  A pharmacoepidemiology example of this is depicted in Figure 1. A patient who receives a prescription may survive longer because he/she must live long enough to receive a prescription while a patient who does not receive a prescription has no survival requirements.  The most common way to avoid immortal time bias is to use a time-varying exposure variable. This allows subjects to contribute to both unexposed (during waiting period) and exposed person time.

 

Figure 1. Immortal Time Bias

Picture2_pharmepi post.png 

Lévesque, Linda E., et al. “Problem of immortal time bias in cohort studies: example using statins for preventing progression of diabetes.” Bmj 340 (2010): b5087.

Protopathic Bias or Reverse Causation

Protopathic bias occurs when a drug of interest is initiated to treat symptoms of the disease under study before it is diagnosed. For example, early symptoms of inflammatory bowel disease (IBD) are often consistent with the indications for prescribing proton pump inhibitors (PPIs). Thus, many individuals who develop IBD have a history of PPI use. A study to investigate the association between PPIs and subsequent IBD would likely conclude that taking PPIs causes IBD when, in fact, the IBD was present (but undiagnosed) before the PPIs were prescribed.  This scenario is illustrated by the following steps:

  • Patient has early symptoms of an underlying disease (e.g. acid reflux)
  • Patient goes to his/her doctor and gets a drug to address symptoms (e.g. PPI)
  • Patient goes on to develop a diagnosis of having IBD (months or even years later)

It is easy to conclude from the above scenario that PPIs cause IBD, however the acid reflux was actually a manifestation of underlying IBD that was not yet diagnosed.  Protopathic bias occurs in this case because of the lag time between first symptoms and diagnosis. One effective way to address protopathic bias is by excluding exposures during the prodromal period of the disease of interest.

 

Drug Exposure Definition and Measurement 

Defining and classifying exposure to a drug is critical to the validity of pharmacoepidemiology studies. Most pharmacoepidemiology studies use proxies for drug exposure, because it is often impractical or impossible to measure directly (e.g. observing a patient take a drug, monitoring blood levels). In lieu of actual exposure data, exposure ascertainment is typically based on medication dispensing records. These records can be ascertained from electronic health records, pharmacies, pharmacy benefit managers (PBMs), and other available healthcare data repositories. Some of the most comprehensive drug exposure data are available among Northern European countries and large integrated health systems such as Kaiser Permanente in the United States. Some strengths of using dispensing records to gather exposure data are:

  • Easy to ascertain and relatively inexpensive
  • No primary data collection
  • Often available for large sample sizes
  • Can be population based
  • No recall or interviewer bias
  • Linkable to other types of data such as diagnostic codes and labs

Limitations of dispensing records as a data source include:

  • Completeness can be an issue
  • Usually does not capture over-the-counter (OTC) drugs
  • Dispensing does not guarantee ingestion
  • Often lacks indication for use
  • Must make some assumptions to calculate dose and duration of use

Some studies collect drug exposure data using self-report methods (e.g. interviews or surveys). These methods are useful when the drug of interest is OTC and thus not captured by dispensing records. However, self-reported data is subject to recall bias and requires additional considerations when interpreting results. Alternatively, some large epidemiologic studies require patients to bring in all their medications when they do their study interviews (eg. bring your brown bag of medications). This can provide a more reliable method of collecting medication information than self-report.

It is also important to consider the risk of misclassification of exposure. When interpreting results, remember that differential misclassification (different for those with and without disease) can result in either an inflated measure of association, or a measure of association that is closer to the null. In contrast, non-differential misclassification (unrelated to the occurrence or presence of disease) shifts the measure of association closer to the null. For further guidance on defining drug exposure, please look at Figure 2.

 

Figure 2. Checklist: Key considerations for defining drug exposure

Picture3_pharmepi post.png
Velentgas, Priscilla, et al., eds. Developing a protocol for observational comparative effectiveness research: a user’s guide. Government Printing Office, 2013.

As alluded to above, pharmacoepidemiology is a field with complex research methods. We hope this article clarifies these three challenging concepts.

 

 

[i](Pinar Balcik, Gulcan Kahraman “Pharmacoepidemiology.” IOSR Journal of Pharmacy (e)-ISSN: 2250-3013, (p)-ISSN: 2319-4219 Volume 6, Issue 2 (February 2016), PP. 57-62)

Is there still value in the p-value?

not sure if significantDoing science is expensive, so a study that reveals significant results yet cannot be replicated by other investigators, represents a lost opportunity to invest those resources elsewhere. At the same time, the pressure on researchers to publish is immense.

These are the tensions that underlie the current debate about how to resolve issues surrounding the use of the p-value and the infamous significance threshold of 0.05. This measurement was adopted in the early 20th century to indicate the probability that the observed results are obtained by chance variation, and the 0.05 threshold has been with it since the beginning, allowing researchers to declare as significant any effect they find that can cross that threshold.

This threshold was selected for convenience in a time when computation of the p-value was difficult to calculate. Our modern scientific tools have made calculation so easy, however, that it is hard to defend a 0.05 threshold as anything but arbitrary. A group of statisticians and researchers is trying to rehabilitate the p-value, at least for the time being, so that we can improve the reliability of results with minimal disruption to the scientific production system. They hope to do this by changing the threshold for statistical significance to 0.005.

In a new editorial in JAMA, Stanford researcher John Ioannidis, a famous critic of bias and irreproducibility in research, has come out in favor of this approach. His argument is pragmatic. In it, he acknowledges that misunderstandings of the p-value are common: many people believe that a result is worth acting on if it is supported by a significant p-value, without regard for the size of the effect or the uncertainty surrounding it.

Rather than reeducating everyone who ever needs to interpret scientific research, then, it is preferable to change our treatment of the threshold signaling statistical significance. Ioannidis also points to the success of genome-wide association studies, which improved in reproducibility after moving to a statistical significance threshold of p < 5 x 10-5.

As Ioannidis admits, this is an imperfect solution. The proposal has set off substantial debate within the American Statistical Association. Bayesians, for example, see it as perpetuating the same flawed practices that got us into the reproducibility crisis in the first place. In an unpublished but widely circulated article from 2017 entitled Abandon Statistical Significance [pdf warning], Blakely McShane, Andrew Gelman, and others point to several problems with lowering the significance threshold that make it unsuitable for medical research.

First, they point out that the whole idea of the null hypothesis is poorly suited to medical research. Virtually anything ingested by or done to the body has downstream effects on other processes, almost certainly including the ones that any given trial hopes to measure. Therefore, using the null hypothesis as a straw man takes away the focus on what a meaningful effect size might be and how certain we are about the effect size we calculate for a given treatment.

They also argue that the reporting of a single p-value hides important decisions made in the analytic process itself, including all the different ways that the data could have been analyzed. They propose reporting all analyses attempted, in an attempt to capture the “researcher degrees of freedom” – the choices made by the analyst that affect how the results are calculated and interpreted.

Beyond these methodological issues, lowering the significance threshold could increase the costs of clinical trials. If our allowance for Type I error is reduced by an order of magnitude, our required sample size roughly doubles, holding all other parameters equal. In a regulatory environment where it costs over a billion dollars to bring a drug to market, this need for increased recruitment could drive up costs (which would need to be passed on to the consumer) and delay the health benefits of market release for good drugs. It is unclear whether these potential cost increases will be offset by the savings of researchers producing more reliable, reproducible studies earlier in the development process.

It also remains to be seen whether the lower p-value’s increased sample size requirement might dissuade pharmaceutical companies from bringing products to market that have a low marginal benefit. After all, you need a larger sample size to detect smaller effects, and that would only be amplified under the new significance thresholds. Overall, the newly proposed significance threshold interacts with value considerations in ways that are hard to predict but potentially worth watching.

Generating Survival Curves from Study Data: An Application for Markov Models

By Mark Bounthavong

Mark_Headshot
CHOICE Student Mark Bounthavong

In cost-effectiveness analysis (CEA), a life-time horizon is commonly used to simulate the overall costs and health effects of a chronic disease. Data for mortality comparing therapeutic treatments are normally derived from survival curves or Kaplan-Meier curves published in clinical trials. However, these Kaplan-Meier curves may only provide survival data up to a few months to a few years, reflecting the length of the trial.

In order to adapt these clinical trial data to a lifetime horizon for use in cost-effectiveness modeling, modelers must make assumptions about the curve and extrapolate beyond what was seen empirically. Luckily, extrapolation to a lifetime horizon is possible using a series of methods based on parametric survival models (e.g., Weibull, exponential). Performing these projections can be challenging without the appropriate data and software, which is why I wrote a tutorial that provides a practical, step-by-step guide to estimate a parameter method (Weibull) from a survival function for use in CEA models.

I split my tutorial into two parts, as described below.

Part 1 begins by providing a guide to:

  • Capture the coordinates of a published Kaplan-Meier curve and export the results into a *.CSV file
  • Estimate the survival function based on the coordinates from the previous step using a pre-built template
  • Generate a Weibull curve that closely resembles the survival function and whose parameters can be easily incorporated into a simple three-state Markov model

Part 2 concludes with a step-by-step guide to:

  • Describe how to incorporate the Weibull parameters into a Markov model
  • Compare the survival probability of the Markov model to the reference Kaplan-Meier curve to validate the method and catch any errors
  • Extrapolate the survival curve across a lifetime horizon

The tutorial requires using and transferring data across a couple of different software. You will need to have some familiarity with Excel to perform these parametric simulations. You should download and install the open source software “Engauge Digitizer” developed by Mark Mitchell, which can be found here. You should also download and install the latest version of R and RStudio to generate the parametric survival curve parameters.

Hoyle and Henley wrote a great paper on using data from a Kaplan-Meier curve to generate parameters for a parametric survival model, which can be found here. The tutorial makes use of their methods and supplemental file. Specifically, you will need to download their Excel Template to generate the parametric survival curve parameters.

I have created a public folder with the relevant files used in the tutorial here.

If you have any comments or notice any errors, please contact me at mbounth@uw.edu